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When Savannah Guthrie wakes up early, it'll be for her daughter--not work.

Though she's currently on maternity leave after welcoming daughter Vale Feldman Wednesday, "Today'"s 42-year-old co-anchor introduced her baby girl to colleagues Matt Lauer and Natalie Morales Thursday. The next morning, Savannah phoned in to the NBC morning show to talk about her new role as a mom.

"Actually, last night I got a good night's sleep for the first time. Vale slept like the true cherubic baby that she is--the little angel baby," she said. Prior to that, Savannah confessed that she'd only slept about one hour in two days, saying, "They actually had to give me a little sleeping medicine so I would calm down."

How is the TV journalist's husband, Mike Feldman, adjusting to life as a first-time father? "You know how fussy he gets!" Savannah said with a laugh. "I've gotta put him down for his nap or he's so cranky."

Regarding her daughter's name, Savannah said, "It's not that much of a story." Prior to delivering Vale, "Today" viewers convinced Savannah that she was having a boy. "I really was shocked when they said, 'It's a girl!'" In fact, she said, "We had a few names on the girl list but we had not really settled on one at all."

"I feel like life just started. Honestly, I just can't get over the joy that she brings," she cooed. "It's kind of inexpressible." From the moment Vale was born, Savannah recalled, she just "cried and cried"--to the point where she "didn't even recognize" the sounds she was making. "It was just like this joy explosion."

"We just cry spontaneously because we love her so much and we're so happy. So I'm a big ball of mush."